FIRST-ORDER ALGORITHM WITH 3 CLUSTERS OF OPTICAL-FLOW VECTORS

The first-order algorithm is an algorithm for recovering the motion pa rameters from a single optical flow field. It compares the spatial der ivatives, to first order, of the optical flow field obtained from two different parts of the field of view and obtains a linear constraint o n the direction of the translational velocity. We modify this algorith m to incorporate the spatial derivatives, to first order, of the optic al flow field obtained from a third part of the field of view, and the reby obtain two further linear constraints on the direction of the tra nslational velocity. Only two linear constraints are required to ident ify the direction of the translational velocity. Therefore, with three linear constraints, there are three ways of estimating the direction of the translational velocity. Although all three estimates are derive d from the same set of information, we show that the three estimates a re not, in general, equally stable. We assume that each cluster of flo w vectors arises from a plane in the environment and show that a linea r constraint is most stable when it emanates from a pair of parallel p lanes, with the camera between them. We also identify the relative ori entations of the clusters of flow vectors that maximize and minimize t he stability of the linear constraint that they give rise to. (C) 1996 John Wiley & Sons, Inc.